Log2(x-3)+log2x-log2(x+2)=2

Answers

Answer 1

We are given the equation:

log₂(x-3) + log₂x - log₂(x+2) = 2

When is it defined:

in this equation, log₂(x-3) and log₂(x+2) can only be defined when

x-3 >0 and x+2 > 0

solving for the values of x, we get:

x > 3    and   x > -2

which basically means x > 3

Because we are looking for an inequality which is true for both x>-2 and x>3

Hence, x will have a value greater than 3

Solving for x:

using the product rule [logₐb + logₐc = logₐ(bc)]

log₂[(x-3)(x)] - log₂(x+2) = 2  

using the quotient rule [logₐb - logₐc = logₐ(b/c)]

log₂[(x-3)(x) / (x+2)] = 2

from the property [ aˣ = b  ⇒  logₐb = x]

(x² - 3x) / (x+2) = 2²

x² - 3x = 4x + 8

x² - 7x - 8 = 0

x² + x - 8x - 8 = 0

x(x+1) - 8(x+1) = 0

(x-8)(x+1) = 0

(x-8) = 0    OR    (x+1) = 0

x = 8      OR      x = -1

We know that the equation is defined only for x > 3

We can see that x = 8 satisfies that inequality

Therefore, x = 8


Related Questions

7 1/5 ÷ 8/1 in simplest form?

Answers

Answer:

9/10 (Decimal: 0.9)

Step-by-step explanation:

7 1/5 ÷ 8 = 9/10

(Decimal: 0.9)

How is the interest rate on a payday loan calculated?
a.
loan amount divided by total fees
b.
total fees divided by loan amount
c.
total fees divided by days of loan
d.
APR divided by 365

Answers

Answer:

b. total fees divided by loan amount

Step-by-step explanation:

The interest rate on a payday loan is usually calculated by dividing the total fees accrued in the loan repayment calculation by the exact loan amount.

Doing this will result in determining the interest rate used in a loan and it’s usually important to ensure accountability and also making sure the exact rate contained in the Loan application agreement Is the same as what is used later on.

Answer:

b. total fees divided by loan amount

Step-by-step explanation:

The interest rate on a payday loan is usually calculated by dividing the total fees accrued in the loan repayment calculation by the exact loan amount.

Doing this will result in determining the interest rate used in a loan and it’s usually important to ensure accountability and also making sure the exact rate contained in the Loan application agreement Is the same as what is used later on.

What is the fourth term in a sequence defined by f(n) = 2n?

Answers

Answer:

8

Step-by-step explanation:

When we look at sequences, we have the function and we have the sequence, the sequence is f(x)... f(n)... or just f with any variable within a parenthesis right next to it.

What the variable signifies is the value that we will be replaced within the sequence, which is 2n in this case. So by your question, it we are looking for the fourth term, that means f(4) = 2n.  Since n is replaced with 4, we do the same with the sequence.

2(4)

Multiply

8

4. Timothy deposited $3500 into an accountthat pays 4.3% simple interest and keeps it
there for 4 years. What is his new account balance after interest?
(8 Points)
$602
$4,102
$6,020
$9,520

Answers

$3,500(4.3%)4= $602

His new account balance after interest is $602

Note: Enter your answer and show all the steps that you please.
Are the ratios 25/45 and 15/27 proportional?

Answers

Yes they are proportional to each other 25/45 =0.5 repeating itself and 15/27 is 0.55 also repeating itself

I hope this help you :) mark me brainiest if u need anything more help like this tell em
yes they are proportional and that’s why ⬇️

learning task 1: identify similar and dissmilar fractions . on your notebook write S if the fractions are similar and D if dissmilar 1. 2/3 and 1/3​

Answers

Answer:

"S" (similar fractions)

Step-by-step explanation:

Since "similar fraction" are those with the same denominator, in our case, since 2/3 and 1/3 have both the same denominator "3", these are similar fractions.

Solve for xRequired to answer. Single choice.Immersive Reader
(5 Points)
6(+2)−20=6
6
(
x
+
2
)

20
=
6
x

No Solution

=−1
x
=

1


=0
x
=
0

all real numbers

Answers

Answer:

the answer is no solution.

Step-by-step explanation:

7a/9bc divided by 21a/12b please I need this answerr

Answers

Answer:

4/9c

Step-by-step explanation:

When dividing by fraction, multiply by its reciprocal.

so 7a/9bc × 12b/21a = 84ab/ 189abc

Simplify

84/189c

4/9c

What property was used to solve the equation?
O Property of opposites
O Division property of equality
* Addition property of equality
O Multiplication property of equality

Answers

Answer:

Multiplication sorry I late

Step-by-step explanation:

Answer: Multiplication property of equality

read the photo and please answer!!
please someone help me answer this and please do give explanation to your answer!

which equation represents the problem?

3x -3 =45

3x = 45 + 3

3 + 3x = 45

3 = 45 + 3x



Now Recipes?

x= 13

x= 15

x= 16

x= 14

Answers

Answer:

3 + 3x = 45 ; x = 14

Step-by-step explanation:

45 = 3x + 3 ⇒ x = 14

2x to the second power + 2 + 9 to the second power

Answers

Answer:

78

Step-by-step explanation:

is it right

im sure it might be 78 the correct

sorry po Bobo po ako sa math ☹️

Step-by-step explanation:

wala eh

Assume there are 11 voting districts in the county.  Polly Tician is running for office. She figures she must win at least 7 of the districts to win the election.  If she has an equal chance of 60% to win any one district, what are her chances of winning the election?

Answers

Answer:

53.3%

Step-by-step explanation:

Here we will use binomial probability:

P = nCr pʳ qⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1−p).

In this case, n = 11, r ≥ 7, p = 0.6, and q = 0.4.

P = ₁₁C₇ (0.6)⁷ (0.4)⁴ + ₁₁C₈ (0.6)⁸ (0.4)³ + ₁₁C₉ (0.6)⁹ (0.4)² + ₁₁C₁₀ (0.6)¹⁰ (0.4)¹ + ₁₁C₁₁ (0.6)¹¹ (0.4)⁰

P = 0.236 + 0.177 + 0.089 + 0.027 + 0.004

P = 0.533

Use benchmark values to estimate 7/10 + 7/8.​

Answers

Answer:

1.575

Step-by-step explanation:

What’s a rationale number ?

Answers

Answer:

A Rational Number can be made by dividing two integers.

(An integer is a number with no fractional part.)

Step-by-step explanation:

Answer:

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

Step-by-step explanation:

Hope this helps. :D

15. Construct Arguments Maggie said that
she could add 8 to both sides of any
equation and the expressions on both sides
of the equation would still be equal. Do you
agree? Explain.

Answers

Answer:

I do not agree because if there is an equation like 7+8 the answers would not be equal. They can only be equal if you add 8 to each side of the same number. For example, 7+7 with 8 added on both sides would be equal. But Maggie says that it can be equal for any equation. Therefore, Maggie is wrong.

Step-by-step explanation:

HELP I NEED TO TURN THIS IN SOON!! WILL GIVE BRAINLIEST!!!

Answers

Answer:

1. 2

2.6

3. 28

4. -10

Step-by-step explanation:

hope this helps

The points A (0,4), B (6, 4) and C (6, -2) are 3 corners of a square ABCD.
What are the coordinates of D, the 4th corner?​

Answers

Answer: It would be (0,-2)

Step-by-step explanation:

WILL MARK AS BRAINLIEST!!!!!

Answers

the answer is Y=2x+1 :)

The graph below shows the cost that Hondo pays for apples. What does the point (0,0) on this graph mean?

Answers

Answer:

(0,0) means that he didn't buy any apples so it doesn't cost anything

Step-by-step explanation:

If f(x) = 16x – 30 and g(x) = 14x – 6, for which value of x does (f – g)(x) = 0? –18 –12 12 18

Answers

Answer:

Option 3: 12 is the correct answer.

Step-by-step explanation:

Given functions are:

[tex]f(x) = 16x-30\\g(x) = 14x-6[/tex]

In order to find the value of x on which (f-g)(x) will be zero, first of all we have to find (f-g)(x) and then equate it equal to zero to find the value of  that will make (f-g)(x)

So,

[tex](f-g)(x) = f(x) - g(x)\\= (16x-30)-(14x-6)\\=16x-30-14x+6\\= 2x-24[/tex]

Now to find the value of x on which (f-g)(x) will be zero, putting (f-g)(x) = 0

[tex](f-g)(x) = 0\\2x-24 = 0[/tex]

Adding 24 on both sides

[tex]2x-24+24 = 0+24\\2x = 24[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2} = \frac{24}{2}\\x = 12[/tex]

For x=12, (f-g)(x) will be zero.

Hence,

Option 3: 12 is the correct answer.

Answer:

C got it right on edge 2022

Step-by-step explanation:

Really bad at math please help

Answers

Answer:

X = 26

Step-by-step explanation:

triangle = 180 degrees

180 - (25+112) = 43

X + 17 = 43

43 - 17 = 26

x = 26

HOPE THIS HELPS

PLZZ MARK BRAINLIEST

PLEASE HELP!

32 = w – 4
1) What is the coefficient?
2) What is the constant?
3) What is the result?
4) What is the variable?

Write a brief paragraph how you would solve the
equation.

Answers

Step-by-step explanation:

coefficient=w

variable=w

result=

32=w-4

w=4+32

w=36

constant=32,4

IF ITS WRONG YOUR BEING REPORTED THIS IS A SERIOUS QUESTION

Answers

Answer:

[tex]range=5.1[/tex]

Step-by-step explanation:

The range of a set is found by subtracting the lowest number from the greatest number.

The greatest number is 2.8 , and the lowest is -2.3. Subtract the values:

[tex]2.8-(-2.3)[/tex]

Two negatives make a positive, so:

[tex]2.8+2.3=5.1[/tex]

:Done

What division problem can be represented using the number line?

A number line going from 0 to StartFraction 10 Over 3 EndFraction in increments of one-third. An arrow goes from 0 to five-thirds and from five-thirds to StartFraction 10 Over 3 EndFraction.
StartFraction 10 Over 3 EndFraction divided by five-thirds
Five-thirds divided by StartFraction 10 Over 3 EndFraction
2 divided by five-thirds
2 divided by StartFraction 10 Over 3 EndFraction

Answers

Answer:

It's the first answer.

Step-by-step explanation:

Answer:

The Answer is A

Step-by-step explanation:

There are 24 balls in gym class. The ratio of basketballs to soccer balls is 2:4. How many basketballs are there? How many soccer balls are there?

Answers

there is 24 basketballs and 48 soccer balls

Given that f(x)= [tex]\frac{x^{2}-3 }{2}[/tex]
A) Find [tex]f^{-1}(x)[/tex]
B) Find [tex]f^{-1} (11)[/tex]
Separate your 2 answers for part B with a comma.
I've solved [tex]f^{-1}(x)[/tex], which was [tex]\sqrt{2x+3}[/tex]

However after this I do not see how I can get another value other than 5.

Answers

Answer:

[tex]x=5,-5[/tex]

Step-by-step explanation:

[tex]\\ y=\frac{x^2-3}{2}\\\\ x=\frac{y^2-3}{2}\\\\ 2x=y^2-3\\\\ y^2=2x+3\\\\ f^{-1}(x)=\pm\sqrt{2x+3}\\\\ f^{-1}(x)=\pm\sqrt{2(11)+3}\\=\pm\sqrt{25}=\pm 5[/tex]

$600 7) Nika puts 42 beads in each necklace. Which is the best way to use rounding numbers to estimate the number of beads Nika needs for 2 necklaces? 25 x 45 O 30 x 30 O 20 x 40 O 30 x 40​

Answers

Answer:

20 X 40 = 800 (split into 2 fourths) = 40

Step-by-step explanation

20 x 40 = 800;

For 2 necklaces she can split 800 into fourths.

800 - 40 = 80. (1 fourth)

80 - 40 = 40 (2 fourths)

40 - 40 = 0 (3 fourths)

She could split 800 into 2 fourths to get a number more than 0 and less then 42.

The best estimate of rounding 42 is 40. Because 40 is closer to 42.

what is the estimate product of 33 and 76

Answers

33 multiplied by 76 is 2,508.

Estimation is ~2,500.

3/4 (x-12) = 12
solve for x

Answers

Answer:

28

Step-by-step explanation:

I got this question on  a test and got it right

HAVE A GREAT DAY!

help⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️​

Answers

Answer:

$1017.19

Step-by-step explanation:

First find the fraction of how much of Paulo's money is spent on his rent and car. Add 1/4 and 1/8, which is 3/8 because 1/4 = 2/8. Then multiply 3/8 by Paulo's monthly spending, which is $2712.50. Multiplying those numbers will get you $1017.1875. which you have to round up to $1017.19 because you can't spend three quarters of a cent.

Answer:

Asumming that you are rounding to the nearest hundreth:

1,017.19

Step-by-step explanation:

Find [tex]\frac{1}{8}[/tex] of 2,712.5 to find how much money Paulo spends on his car.

[tex]\frac{1}{8}[/tex] = .125

Multiply 2,712.5 by .125

2,712.5 × .125 = 339.0625 ≈ 339.06

Now, find [tex]\frac{1}{4}[/tex] of 2,712.5 to find how much paulo spends on his rent.

[tex]\frac{1}{4}[/tex] = .25

Multiply 2,712.5 by .25

2,712.5 × .25 = 678.125 ≈ 678.13

Add the two values together to get your answer

339.09 +

678.13

----------

1,017.19

(Another way to dolve this problem would be to find [tex]\frac{5}{8}[/tex] of 2,712.5 and subtract it from the origional value, 2,712.5)

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